Snyder dynamics in a Schwarzschild spacetime

Abstract

We calculate the orbits of a particle in Schwarzschild spacetime, assuming that the dynamics is governed by a Snyder symplectic structure. With this assumption, the perihelion shift of the planets acquires an additional contribution with respect to the one predicted by general relativity. Moreover, the equivalence principle is violated. If one assumes that Snyder mechanics is valid also for macroscopic systems, these results impose strong constraints on the value of the coupling parameter of the Snyder model.

7 pages

References in corpus (24)

• The Confrontation between General Relativity and Experiment
• Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
• Classical and quantum mechanics of the nonrelativistic Snyder model
• Triply Special Relativity
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry
• Multi-Particle States in Deformed Special Relativity
• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• Snyder noncommutative space-time from two-time physics
• Scalar field theory in Snyder space-time: alternatives
• Snyder space revisited
• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
• Linear Form of 3-scale Relativity Algebra and the Relevance of Stability
• Particle Dynamics on Snyder space
• Doubly special relativity and translation invariance
• The Soccer-Ball Problem
• Classical dynamics on curved Snyder space
• The Area Quantum and Snyder Space
• Symmetries of Snyder--de Sitter space and relativistic particle dynamics
• The Kepler problem in the Snyder space
• Snyder-de Sitter model from two-time physics
• Coherent States for 3d Deformed Special Relativity: semi-classical points in a quantum flat spacetime
• The Atick-Witten free energy, closed tachyon condensation and deformed Poincare' symmetry
• Classical dynamics on Snyder spacetime

Cited by in corpus (19)

• Generalized Uncertainty Principle, Classical Mechanics, and General Relativity
• Quantum field theory in generalised Snyder spaces
• Bumblebee gravity and particle motion in Snyder noncommutative spacetime structures
• Associative realizations of the extended Snyder model
• Heisenberg doubles for Snyder type models
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Macroscopic body in Snyder space and minimal length estimation
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Twist for Snyder space
• Minimal length estimation on the basis of studies of the Sun-Earth-Moon system in deformed space
• Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
• Kinetic energy properties and weak equivalence principle in a space with GUP
• Black hole thermodynamics in Snyder phase space
• Realizations of the Extended Snyder Model
• Snyder Like Modified Gravity in Newton's Spacetime
• Snyder and their representation with creation and annihilation operators
• Some features of a Schwarzchild Black Hole from a Snyder perspective
• Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism